Download Elimination Using Multiplication Study Guide

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Elimination Using Addition and Subtraction Study Guide
Some systems can be combined in order to cancel out a variable so that the solution can be
found. Consider the following example.
Example: Use elimination to solve the system of equations
x + 2y = 2 and -x + 5y = 5
x + 2y = 2
-x + 5y = 5
7y = 7
y=1
1. Rewrite both equations in slope-intercept form.
2. Add or subtract to cancel out one variable.
3. Solve for the variable remaining.
4. Substitute 1 for y into either equation and solve for x.
x + 2(1) = 2
x+2=2
x=0
The solution of the system is (0, 1).
Use elimination to solve each system of equations.
1.
3x + 2y = 0
-3x – 5y = 9
2. 2x + -2y = 6
2x + 2y = 2
3. 3x – y = 2
x + y = 10
4. 2x + 3y = 5
-x + 3y = -7
5. 4x + y = 4
-4x + y = -12
6. 5x – 2y = -18
-3x – 2y = 14
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Period:
Use elimination to solve each system of equations.
7. 7x – 8y = -2
5x + 8y = 26
8. 4x – 2y = -10
3x – 2y = -8
9. 5x + 3y = -9
5x + 5y = -5
10. 2x + 3y = -2
5x + 3y = 4
Substitution Review: Use the substitution method to solve each system of equations.
11. x + 4y = 8
2x – 5y = 29
12. 4x + y = 0
x + 2y = -7
13. 2x – 3y = -9
x + 6y = 18
14. x + 14y = 84
2x – 7y = -7
15. x = 3
2y + x = 3
16. x – 3y = -4
2x + 6y = 4